As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:
Yuta has a non-direct graph with $n$ vertices and $m$ edges. The length of each edge is 1. Now he wants to add exactly an edge which connects two different vertices and minimize the length of the shortest path between vertice 1 and vertice $n$. Now he wants to know the minimal length of the shortest path and the number of the ways of adding this edge.
It is too difficult for Rikka. Can you help her?
Input
There are no more than 100 testcases.
For each testcase, the first line contains two numbers $n,m(2 \leq n \leq 100, 0 \leq m \leq 100)$.
Then $m$ lines follow. Each line contains two numbers $u,v(1 \leq u,v \leq n)$ , which means there is an edge between $u$ and $v$. There may be multiedges and self loops.
Output
For each testcase, print a single line contains two numbers: The length of the shortest path between vertice 1 and vertice $n$ and the number of the ways of adding this edge.
